{
  "id": "wh-to-ah",
  "version": "3a1532d9ba91",
  "status": "published",
  "name": "Wh to Ah Calculator",
  "question": "Wh to Ah: how many amp hours?",
  "summary": "Converts watt hours to amp hours at a battery’s voltage, Ah = Wh ÷ V, and back, Wh = Ah × V, with mAh and kWh; or finds the voltage from Wh and Ah.",
  "category": "physics",
  "subcategory": "electricity",
  "url": "https://www.acalculator.org/physics/wh-to-ah-calculator",
  "markdown": "https://www.acalculator.org/physics/wh-to-ah-calculator.md",
  "kind": "function",
  "method": "Ah = Wh ÷ V; Wh = Ah × V; V = Wh ÷ Ah. 1 Ah = 1,000 mAh; 1 kWh = 1,000 Wh.",
  "assumptions": [
    "The voltage is the battery’s nominal (average) voltage; the real voltage falls as a battery drains.",
    "Typed values are read as the exact decimals you typed; each result is rounded once to show."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "What to work out: amp hours from watt hours, watt hours from amp hours, or the voltage.",
        "type": "string",
        "enum": [
          "ah",
          "wh",
          "volts"
        ]
      },
      "wh": {
        "title": "Energy (Wh)",
        "description": "The battery’s energy in watt hours or kilowatt hours.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "energy",
        "minimum": 3.6e-9,
        "maximum": 3600000000000000
      },
      "v": {
        "title": "Voltage (V)",
        "description": "The battery’s nominal voltage.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "minimum": 1e-9,
        "maximum": 1000000000
      },
      "q": {
        "title": "Charge",
        "description": "The battery’s capacity in amp hours or milliamp hours, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-12,
        "maximum": 1000000000000
      },
      "qu": {
        "title": "Charge unit",
        "description": "Amp hours (Ah) or milliamp hours (mAh): 1 Ah = 1,000 mAh.",
        "type": "string",
        "enum": [
          "Ah",
          "mAh"
        ]
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value found, to 6 significant figures, with a second unit for amp hours and watt hours.",
      "format": "text"
    },
    "ah": {
      "label": "Charge, Ah",
      "description": "The capacity in amp hours: Wh ÷ V.",
      "format": "number"
    },
    "mah": {
      "label": "Charge, mAh",
      "description": "The capacity in milliamp hours: Ah × 1,000.",
      "format": "number"
    },
    "wh": {
      "label": "Energy, Wh",
      "description": "The energy in watt hours: Ah × V.",
      "format": "number"
    },
    "kwh": {
      "label": "Energy, kWh",
      "description": "The energy in kilowatt hours: Wh ÷ 1,000.",
      "format": "number"
    },
    "volts": {
      "label": "Voltage, V",
      "description": "The voltage: Wh ÷ Ah.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "ah",
      "wh": "100 Wh",
      "v": "12 V",
      "q": 10,
      "qu": "Ah"
    },
    "outputs": {
      "result": "8.33333 Ah (8,333.33 mAh)",
      "ah": 8.333333333333334,
      "mah": 8333.333333333334,
      "wh": 100,
      "kwh": 0.1,
      "volts": 12
    },
    "text": "100 Wh at 12 V is 8.33333 Ah (8,333.33 mAh)."
  },
  "examples": [
    {
      "given": {
        "find": "ah",
        "wh": 360000,
        "v": 12
      },
      "expect": {
        "ah": 8.333333333333334,
        "mah": 8333.333333333334,
        "result": "8.33333 Ah (8,333.33 mAh)"
      },
      "source": "NIST Special Publication 811 (2008), Chapter 4, Table 3: the volt is W/A, the coulomb s·A, the watt J/s, https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-4-two-classes-si-units-and-si-prefixes (retrieved 2026-10-19); NIST Special Publication 811, Appendix B.8: ampere hour = 3.6 × 10³ C and watt hour = 3.6 × 10³ J, exact, https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19); hand calculation in content.mdx: 100 ÷ 12 = 8.33333 Ah"
    },
    {
      "given": {
        "find": "wh",
        "q": 5000,
        "qu": "mAh",
        "v": 3.7
      },
      "expect": {
        "wh": 18.5,
        "kwh": 0.0185,
        "ah": 5,
        "result": "18.5 Wh (0.0185 kWh)"
      },
      "source": "NIST Special Publication 811 (2008), Chapter 4, Table 3: the volt is W/A, the coulomb s·A, the watt J/s, https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-4-two-classes-si-units-and-si-prefixes (retrieved 2026-10-19); hand calculation in content.mdx: 5,000 mAh = 5 Ah, 5 × 3.7 = 18.5 Wh"
    },
    {
      "given": {
        "find": "volts",
        "wh": 180000,
        "q": 4000,
        "qu": "mAh"
      },
      "expect": {
        "volts": 12.5,
        "result": "12.5 V"
      },
      "source": "NIST Special Publication 811 (2008), Chapter 4, Table 3: the volt is W/A, the coulomb s·A, the watt J/s, https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-4-two-classes-si-units-and-si-prefixes (retrieved 2026-10-19); hand calculation in content.mdx: 50 Wh ÷ 4 Ah = 12.5 V"
    },
    {
      "given": {
        "find": "ah",
        "wh": 48600000,
        "v": 48
      },
      "expect": {
        "ah": 281.25,
        "wh": 13500,
        "result": "281.25 Ah (281,250 mAh)"
      },
      "source": "NIST Special Publication 811 (2008), Chapter 4, Table 3: the volt is W/A, the coulomb s·A, the watt J/s, https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-4-two-classes-si-units-and-si-prefixes (retrieved 2026-10-19); NIST Special Publication 811, Appendix B.8: ampere hour = 3.6 × 10³ C and watt hour = 3.6 × 10³ J, exact, https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19); hand calculation in content.mdx: 13,500 Wh ÷ 48 V = 281.25 Ah"
    }
  ],
  "sources": [
    "NIST Special Publication 811 (2008), Chapter 4, Table 3 (the 22 SI coherent derived units with special names): the volt is W/A, the coulomb s·A, the watt J/s, retrieved 2026-10-19. https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-4-two-classes-si-units-and-si-prefixes",
    "NIST Special Publication 811, Appendix B.8: ampere hour (A·h) = 3.6 × 10³ C, watt hour (W·h) = 3.6 × 10³ J and kilowatt hour = 3.6 × 10⁶ J, all exact, retrieved 2026-10-19. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8"
  ],
  "related": [
    "battery-life",
    "amp",
    "wattage",
    "power"
  ],
  "changelog": []
}